Intelligent modeling and optimization of titanium surface etching for dental implant application

Acid-etching is one of the most popular processes for the surface treatment of dental implants. In this paper, acid-etching of commercially pure titanium (cpTi) in a 48% H2SO4 solution is investigated. The etching process time (0–8 h) and solution temperature (25–90 °C) are assumed to be the most effective operational conditions to affect the surface roughness parameters such as arithmetical mean deviation of the assessed profile on the surface (Ra) and average of maximum peak to valley height of the surface over considered length profile (Rz), as well as weight loss (WL) of the dental implants in etching process. For the first time, three multilayer perceptron artificial neural network (MLP-ANN) with two hidden layers was optimized to predict Ra, Rz, and WL. MLP is a feedforward class of ANN and ANN model that involves computations and mathematics which simulate the human–brain processes. The ANN models can properly predict Ra, Rz, and WL variations during etching as a function of process temperature and time. Moreover, WL can be increased to achieve a high Ra. At WL = 0, Ra of 0.5 μm is obtained, whereas Ra increases to 2 μm at WL = 0.78 μg/cm2. Also, ANN model was fed into a nonlinear sorting genetic algorithm (NSGA-II) to establish the optimization process and the ability of this method has been proven to predict the optimized etching conditions.

Creating rough surfaces on medical implants has been shown to improve their bio-integration resulting from increased bone tissue production at the modified surfaces [1][2][3][4] . Many studies have shown that undesirable fibrous tissues tend to form on smooth surfaces, while rougher surfaces promote the formation of solid bone tissue 5,6 conducted a long-term study of bone integration with implants 7,8 . Bone is generated in a multistep process wherein osteoclast cells selectively remove tissue to form pits (lacunae), and the osteoblast cells, in turn, collect and form the bone matrix tissues 9 . As osteoclasts cannot interact with implant materials, such as titanium (Ti), osteoblast bonding can be inhibited if an implant's surface does not possess micro-, meso-, ornano-scale structures similar to those created by osteoclasts 10 .
Usually, surface roughness is checked with some parameters like R a , R z , and S a . R a is a 1-D parameter and is defined as arithmetical mean deviation of the assessed profile 11 . For measurement of R a , a very thin detector tip moves in a horizontal linear direction over the surface of the sample (in contact or noncontact mode), that vertical moves will be reported 12,13 . R z is maximum peak to valley height of the same profile, that is studied for R a measurement 12 . S a is an areal roughness parameter that is detected from a 2-D surface (unlike Ra that is detected from a linear path) 11 . Based on definitions, R a and S a are very close to each other and choosing one of them is based on measurement equipment (some of them report R a and some other report S a ) 11,12 . Etching is one of the most popular processes used to enhance surface roughness and improve other properties of the surface. It is responsible for enhancing a dental implant's contact with bone and can specify the strength of the implant's contact with the surface [11][12][13][14][15] and bone response [16][17][18][19][20] . Currently, a wide range of commercial dental implants is available in the market. These implants have differing properties, such as the implant's core, geometric specifications, and surface characteristics. Some commercial brands, such as Ospol (Hollviken, Sweden), with S a = 0.26 μm, have a smooth surface (S a < 1 μm is considered smooth) 21 . On the other hand, other commercial implants, such as SLA (Standard Plus; ITI Straumann, Basel, Switzerland; S a = 1.7 μm), Ankylos (Dentsply-Friadent, Menheim, Germany; S a = 1.55 μm), Frialit (DentsplyFriadent, Menheim, Germany; S a = 1.79 μm), and Promote (Screwline, calmog, Basel, Switzerland; S a = 1.30 μm), are moderately rough (with S a in the range of 1-2 μm) 22,23 . Additionally, some other surfaces, such as the Kohno HRPS and Kohno DES HRPS (Sweden & Martina, Due Carrare, Italy; S a = 3.11 and 3.16 respectively), have the highest degree of roughness (surfaces with S a > 2 are considered maximally rough) 22,23 .
In 2010, Elias 24 reported that acid-etched implants have a more homogeneous surface compared to machined surfaces. In addition, the acid etching process, when applied as a pretreatment for anodizing the dental implants (or other processes), provides homogeneous roughness, a large active surface area, and improves bio-adhesion. Grizon and coworkers 25 conducted a long-term study to investigate the enhancement of bone-implant integration with increased surface roughness. No significant differences were observed for the two types of implants between 3-6 months. At 12 and 18 months, the bone volume and contact interface were still increasing, and the implants with R a = 0.206 µm were associated with higher values than the smoother implants (R a = 0.160). Many similar studies, such as one by Fouziya et al. 26 reported that, smoother surfaces require a longer time for osseointegration and prosthetic loading.
The trends in dental implant surface modifications can be classified into the five generations shown in Fig. 1a. Etching was part of the first generation of methods for improving machined surfaces with mechanical treatment. Despite all the improvements to surface modification methods, etching is still widely used in commercial systems, either directly as a final surface modification or in combination with other methods. Based on Fig. 1b, after the plasma spray coating process, etching, with a more than 15% usage rate, is the second most used method based on published reports. In addition, several of the other methods, like sandblasting and sandblasting plus acid etching (SLA), use etching as a treatment method 27 .
Acid etched has a lower risk of implant surface contamination than blasting since there are no particle remnants on the surface 28 . This surface enhances the migration and retention of osteogenic cells. There are variations in acid etching methods between the different manufacturers based on acid concentration, process time, and temperatures. Acid etching forms micropits on the implant surface 29 and titanium hydrides that are replaced by oxygen, slowing the transformation of the implant surface. In addition, nanosized titanium particles are formed on the surface that favor the adhesion of proteins through surface nano-roughness features 30 . Acid-etched surfaces show more bone apposition, increasing the interfacial strength as calculated by removal torque [31][32][33] or push-out tests 14,34 . Moreover, etching the dental implant surfaces leads to a reduction in the healing time in the mandible and the maxilla at 6-8 weeks (from 3-6 months) [35][36][37][38] .
Mathematical models for etching process can lead to choosing suitable operation condition and having desirable surface for dental implants. Between different methods of modelling, artificial neural networks (ANN) have many advantages over others and intelligent modelling using experimental datasets for model configuration have more reliability. ANNs are a technology based on the studies of the nervous system and brain. These networks emulate a biological neural network but they use a reduced set of concepts from biological neural systems. Specifically, ANN models simulate the electrical activity of the brain and nervous system. Processing elements (also known as either a neuron or perceptron) are connected to other processing elements. Typically, the neuron is arranged in a layer or vector with the output of one layer, serving as the input to the next layer and possibly other layers. A neuron may be connected to all or a subset of the neuron in the subsequent layer. Weighted data signals entering a neuron simulate the electrical excitation of a nerve cell and consequently, the transference of information within the network or brain. Output of this data transfer between neurons, is processing on the data and prediction of output. ANN model should be optimized by training, validation and test [39][40][41][42] . Despite all advantages of ANN, a reliable model is needed to correct experimental datasets and collection of suitable data in appropriate number, that is costly and time consuming.
Numerical study of surface characteristics for dental implant application, is relatively new field of study. In 2020, Kohler et al. 43 reported a numerical model for titanium acid etching. Their model assumed R a to be the only determining parameter. Weight loss as a parameter of geometrical limitations should be fixed in an acceptable range (based on quality control protocols). Intelligent modeling with artificial neural networks (ANN) can address the drawbacks of the other methods of modelling such as the inability to fit large amounts of data. Therefore, multilayer perceptron (MLP) ANN is used to model the etching process in 48% H 2 SO 4 solution. In the following, nonlinear sorting genetic algorithm (NSGA-II) optimization method is utilized to arrive at the optimal conditions for the process.

Materials and methods
In this study, MLP-ANN was used to investigate the surface characteristics including the R a , R z , and WL when etching solution temperature and etching process time varies. A MLP-ANN with two hidden layers was used for achievement to the optimized topology of ANN, 1 to 5 neurons were tested in each hidden layer. Finally, ANN structure with lowest MSE was proposed as the best ANN model and fed to the NSGA-II for process optimization.
Ban et al. 44 investigated etching time and etching solution media temperature effects on surface characteristics. Data were feeding into ANN models. The following equation [Eq. (1)] was used to normalize input variables in rang of [-1, + 1]: where Xi is a normalized value of input variable xi, x min is minimum value of target functions and x max is the maximum one 39,45 .
(1) www.nature.com/scientificreports/ An in-house computational code was developed in this study that can conceptually search for best ANN configurations with dividing data into 'training' , 'validation' , and 'test' sets. Accordingly, 70% of data was randomly chosen to train the model. On the other hand, 15% of data was fed to ANN model for validation. Finally, the rest of the data was used for testing the configured ANN structure. Although there is no rigid rule to find the appropriate number of neurons in the hidden layers, the complexity of the relationship between inputs and outputs plays a key role 46,47 . Different combinations of neurons (one to five neurons in each hidden layer) in two hidden layers were tested for choosing the best configuration with a minimized error. The function defined through Eq. (2) was applied in output, and hidden layers were used as activation transfer function 40,48 : A well-organized in-house code based on the flowchart illustrated in Fig. 2 was used to model R a , R z , and WL (three different models). A gradient descent (G.D.) method was used to model optimization parameters and find the best biases and weights to match the input and output variables.
Number of neurons in hidden layer 1 and hidden layer 2 varied in range of 1 to 5 (max NH1 and max NH2 is equal to 5). Model accuracy for response prediction was measured by mean of squared error (MSE) criterion 49,50 as noted in Eq. (3) 39,46,47,51 .

Biochemical active surface
Immobilization of collagen, BMP, peptide, gelatin etc.

Physicochemical active surface
HA coating, alkaline treatment etc.

Morphological surface
Blast, Groove, Etching, Anodic oxidation etc. To reach the desirable model the inputs must be normalized and also activation transfer function should be used for output and hidden layers. Several types of activation transfer function are utilized. Three of these functionsaremore important and applicable that shown in Fig. 3; Pureline [Eq. (4)], Logsig [Eq. (5)], and Tansig [Eq. (7)].

• Linear transfer function (Purelin)
This transfer function is regularly employed in the output layer. The primary interest of MLPs resides in their nonlinear sigmoid function (such as logsig and tansig) principally used in their hidden layers.
• Log-Sigmoid transfer function (Logsig) www.nature.com/scientificreports/ which is easily differentiable, and frequently used as a nonlinear transfer function for engineering applications. However, because it is limited between 0 and 1, its linearly transformed type is used instead. It is recognized as the bipolar transfer function [Eq. (6)]: • Hyperbolic Tangent Sigmoid (Tansig) which is very alike in kind and shares many mathematical properties with the bipolar transfer function and it is bounded between − 1 and + 1. It is too often employed in engineering application.
In the light of the above procedure, three ANN modelswere optimized to investigate the effective parameters on surface properties (R a , R z , and WL). In the next step, for the multi-objective optimization of the etching process in 48% H 2 SO 4 solution, a Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) was utilized. For the production of chromosomes, the value of each gene was randomly chosen in view of the values of variables given in Table 1. The code was then implemented to find the fitness of each chromosome to optimize surface properties simultaneously. After giving pairs of chromosomes were compared together, they were isolated from the remainder, as the first Pareto front. This operation was surveyed to obtain Pareto fronts 2, 3, etc. Pareto front n was assigned to the chromosome that has been dominated (n − 1) times. We also used crowding distance (C.D.) values, as the second criterion for optimization, was to sort pareto fronts [Eq. (8)]: where In Eq. (8), N is the number of objective functions, C.D. (i) is the crowding distance of the chromosome i, and d x (i) and Δ x (i) are based on the objective function x, as shown in Fig. 4a. After estimating the degree of fitness   www.nature.com/scientificreports/ based on primary and secondary constraints, chromosomes were sorted according to their favorability. The best chromosomes were chosen as the first Pareto front, followed by selecting, pairing, reproducing, and muting. The fitness of the parents and of the children of the new generation was revisited by utilizing a non-dominated sorting algorithm. Table 1 gives the values of parameters employed to optimizethesurface properties based on the NSGA-II evolutionary algorithm (Fig. 4b).

ANN-based model evaluation. R a ANN structure configuration and model validation.
The ANN-based model evaluation for the R a was completed in the first step. As shown in Fig. 5, an ANN model with two hidden layers (three neurons in the first hidden layer and one neuron in the second hidden layer) was the best structure for R a prediction based on temperature (°C) and time (h) variation. Different combinations of Tansig and Logsig transfer functions were approved, and the results showed that the Tansig transfer function for both hidden layers performed best. The correlation coefficient (R) for the fixed ANN model, was 0.9892 that is very close to 1; this indicated that the model is reliable. In the following, the accuracy of the model was studied by the quality line. As illustrated in section (a) of Fig. 6, the model fit is perfect if all the predicted data equals the experimental data. Therefore, the model has high accuracy if all data fall close to the y = x line. The ANN model predicted the experimental data with less than 10% error (see Fig. 6). As a result, the configured model was used to predict R a under different operational R z ANN structure configuration and model validation. The second ANN model was configured to predict R z on the titanium surface during acid etching with 48% H 2 SO 4 with etching time and solution temperature variation. The best ANN structure was obtained by an ANN model with two neurons and four neurons in the first and second hidden layers, respectively. The best transfer function for the first hidden layer was Logsig, while Tansig emerged as the best transfer function for the second hidden layer. A schematic structure of the optimized ANN model is presented in Fig. 7.  www.nature.com/scientificreports/ The ANN model accuracy for R z prediction was further evaluated by calculating R, error, and the quality line. The optimized ANN model for R z prediction had a correlation coefficient of about 0.9970. The quality line and error diagram showed that the chosen ANN model predicted the experimental data with suitable accuracy (see Fig. 8a,b). As shown in the error diagram, all data was predicted with minimal error (less than 10%). The validated model was then used to calculate R z under different conditions. The pattern of R z variation based on etching time in different etching media temperatures (25,30,40,50,60,70,80, and 90 °C) is shown in Fig. 8c.  www.nature.com/scientificreports/ tion of transfer functions for the first and second hidden layers. A schematic of the optimized ANN topology is illustrated in Fig. 9. Comparison of experimental data with ANN-based WL predictions showed good accuracy with a correlation coefficient of 0.9991. The quality line and prediction error are presented in Fig. 10a Figure 9. A schematic ANN model structure for WL prediction based on etching time and solution temperature. www.nature.com/scientificreports/ hand, studies showed that a higher R a can improve an implant's survival rate. Higher removal torque 52 is accessible through higher R a , while higher surface roughness is the main factor responsible for enhancing surface area. Higher surface areas can improve the chances of bone cell growth on the titanium implant surfaces 27,53 . Therefore, the main goal of the etching process is to increase the surface roughness and decrease WL simultaneously. Unfortunately, there is a tradeoff between WL and surface roughness. Higher surface roughness is achieved at longer etching times and higher etchant temperatures, but these same conditions can increase WL. High temperatures and extended etching times can damage the substrate and change its geometric parameters. The surfaces of commercial dental implants have different surface roughnesses in the range of 0.5 to less than 4 µm 21,54,55 . Surfaces with a roughness level higher than 2 µm are very limited and commonly produced by special processes, such as laser-based surface treatment methods 55,56 . On the other hand, machined surfaces of titanium-based implants are not perfectly smooth. Machined surfaces have a roughness of about 0.5 µm. On the commercial scale, surface roughnesses in the range of 0.5-2 µm are common. Therefore, multi-objective optimization was performed to minimize WL and maximize R a (Fig. 11a), R a = 0.5 (Fig. 11b), R a = 1 (Fig. 11c), R a = 1.5 (Fig. 11d), and R a = 2 µm (Fig. 11e). In all cases, the tradeoff between R a and WL is evident: higher R a values lead to higher WL, and lower WL is achieved at lower R a .
Acid etching is a common base method for subsequent surface treatment processes, such as anodizing. Previous studies have shown that the roughness of etched surfaces is effective on the final treated surface of titanium 53,57 . Therefore, the best condition for the etching process is dependent on the treatment processes that follow it. However, some points with infinite C.D. are presented in Table 2.
As noted in Table 2, higher temperatures and longer etching times are required to achieve higher R a values. On the other hand, the lowest WL is achieved at the lowest process temperatures and shortest etching times. Therefore, objects with infinite C.D. can lead to a point with high R a and high WL and another point with minimized WL and very low roughness (see Table 2). As noted in the previous sections, machined titanium substrates have an R a of about 0.5 µm. Optimizing the ANN model at R a = 0.5 µm for the lowest WL value leads to operating conditions with the lowest temperature and a process time close to 0 h. Moreover, the best route to achieving a R a value of 2 µm was an operating temperature of 54.12 °C and an etching time of 3.62 h. Under these conditions, the lowest WL achieved is about 1.96 µg/cm 2 .
Optimization of R a and R z . Homogeneity is a target parameter for surfaces in dental implant production. Homogeneity has several effects on the characterizations of dental implant surfaces and the production process 58,59 . Achieving a perfectly reproducible product is dependent on the production of homogeneous surfaces. Variation of characteristics from point to point or product to product is very high in heterogeneous surfaces. One element of surface homogeneity is approaching the R z to R a . It is clear that R z is usually much more than R a . On the other hand, the difference between R a and R z is not a surface recognition factor as being heterogeneous. However, a surface with R z close to the R a value is considered more homogeneous than a surface with R z far removed from the R a value. All surfaces in this study have an R z higher than 3 µm, which is higher than the R a values. Figure 12a shows that the R z of the H 2 SO 4 -etched titanium surface was altered from lower than 4 to about 18. The first objective was to minimize the R z and maximize the R a (Fig. 12a). The optimization to minimize R z at R a = 0.5, Ra = 1, R a = 1.5, and R a = 2 are presented in Fig. 12b-e. Some points with infinite C.D. and their operating conditions are noted in Table 3. From Table 3, we can see that the lowest achievable R z is a little lower than 4 µm. At this point, a minimized R a will be obtained. On the other hand, a maximized R z is obtained (higher than 18 µm) under harsh process conditions that lead to the highest R a (about 3.5 µm).

Discussion
The surface characteristics of dental implants affect the osseointegration process and implant survival rate. In this context, a surface treatment process that affects implant surface composition, surface roughness, and surface homogeneity is vital to developing new surfaces that facilitate osseointegration. This study provides a novel approach to using the ANN and NSGA-II to model and optimize the dental implant etching process. ANN optimizations, such as the one used in this study, have previously been used in other fields, such as surface roughness optimization of magnesium alloy machining 60 and finish turning of AISI 4140 hardened steel 61 .
Three ANN models were developed to predict R a , R z , and WL based on H 2 SO 4 temperature and etching duration. In agreement with previous studies, all the correlation coefficients were above 0.98. Therefore, the ANN models predicted the experimental data with a high degree of accuracy. Abbas et al. 60 showed that when the correlation coefficient of ANN model was 0.986, high accuracy of their model in predicting surface roughness was achieved. In other study, Meddour et al. 61 used an ANN model with correlation coefficient of 0.99 for R a predicting. Therefore, the configured ANN models for R a (R = 0.9892), R z (R = 0.9970) and WL (R = 0.9991), are reliable. Results of this study showed that the etching process can increase the surface roughness. Lazzara et al. 62 compared the bone response of a dual-etched surface to machined implants in the human posterior maxilla. After a healing time of six months, bone contact at the etched surface and the machined surface were 72.96% and 33.98% respectively. Additionally, a unique feature was detected at the etched surface that is bone creeping along the surface. The osteoconductive effect of the etch-textured surface over the machined surface, was particularly pronounced in the softer trabecular bone. In this type of bone, the amount of bone apposition was enhanced from 6.5 ± 10.8% for the machined surface to 59.1 ± 25.3% for the etched surface.
Low removal torque is a fundamental problem in some dental implant with relatively smooth surfaces. Low removal torque can lead to in place rotation of dental implant in prosthetic loading. Higher roughness can increase needed removal torque that can be achieved by etching process in the conditions resulted in this study. Klokkevold et al. 52 investigated the anchoring of the etched and machined surfaces on rabbit tibia after one, two and three months. After one month, the mean removal torque of the machined surface was 6.00 ± 0.64 N cm, Surface roughness as one of the most important parameters that is effective in dental implant performance, have been studied in this research. Reports suggest that surface roughness is not the only effective surface parameter that determines the implant's survival rate and osseous contact. Based on the clinical experiments, acid-etched titanium (SLA) promotes a greater and more rapid osseous contact when titanium-plasma-sprayed implants are used 33,64 . Surface hydrogen concentration and the formation of titanium hydride 65 , surface topology 44,66 and surface wettability 67 are some other parameters that are improved through the acid etching process.
In advanced dental implant surface treatment methods like SLA, a combination of air-abrasion parameters and acid etching variables can specify the final properties of the surface. After optimizing surface roughness by varying the acid etching parameters, we will study the sandblasting process. In future studies, we are interested in exploring the effect of different sand particle shapes on the surface configurations of dental implants. In addition, gas flow velocity, pressure, temperature, particle size, size distribution, and particle nature may also influence the final surface characteristics. However, since surface properties can be altered in the etching step, the outcomes of both treatments need to be considered to achieve the most favorable results.

Conclusions
We evaluated the impact of etching solution temperature and etching process time on the surface characteristics (R a , R z , and WL) of dental implants in an acidic solution containing 48% H 2 SO 4 . The results showed that increasing both temperature and process time can enhance R a , R z , and WL. In addition, results confirmed the ability of an MLP-ANN model to predict the surface characteristics as a function of the etching parameters. Increasing the etching process time leads to higher R a , R z and WL values. Based on the MLP-ANN predictions, increasing etching time at higher etching solution temperatures is more effective for improving the surface characteristics. In the following, NSGA-II based multi-objective optimization was used for obtaining the optimum time of etching and temperature of etching solution with the aim of minimizing the W L and R z and maximizing the R a . Finally, the results showed that the NSGA-II based optimization could be successfully applied for MLP-ANN based modeled etching process that could be used in dental implant surface treatment. Regarding the obtained results, ANN based models can be used for next studies of surface characteristics modelling. In addition, NSGA-II based multi-objective optimization can be successfully applied for prediction of the ideal operation condition, having the best surface. www.nature.com/scientificreports/ Figure 12. Multi-objective optimization of R a and R z in the etching of titanium to achieve (a) maximized R a and minimized R z , (b) fixed R a = 0.5 and minimized R z , (c) fixed R a = 1 and minimized R z , (d) fixed R a = 1.5 and minimized R z , and (e) fixed R a = 2 µm and minimized R z .